Lashing on (also called lacing on) has some of good advantages: it doesn't use as much warp as tying does and so is good for scant, expensive, or handspun warp; it's good for slippery warps; or for warps that are so dense as to crowd the apron rod when tied on.
The disadvantage is that it requires a stout, smooth cord about ten times the width of the warp for lacing. It's also a nuisance to correct threading errors, but these are a nuisance anyway, in my opinion.
When I started my series of afghans, I discovered that I didn't have a lashing cord ten times the 44 inch width of the warp. All of my lashing cords were considerably shorter. I suppose I could have waited until I could get more cord, but being the impatient sort who was really chomping at the bit to start weaving on my new loom, I decided to tie the warp on.
To my delight it worked quite well. The warp behaved, the tension behaved, and the knots behaved. As I've woven my way through several afghans, I've tied each warp onto the front apron rod.
At first I thought that my success was due to the fact that I have quite a bit more weaving experience under my belt than the last time I tried tying. But as I reflected, I realized that a lot of my problem back then had been due to the type of yarn I was weaving with: rayon. Rayon is slippery! But I had gotten a bunch of rayon yarn really cheap (as in a dollar a cone) so I used it. Lashing on improved my tension problems, and when I switched to cotton yarns I lashed them on too.
The acrylic yarns I've been using for the afghans tie on nicely. The yarn grips well, so that I only need a half knot as I'm tensioning the warp. (On the other hand, the warp for the wool afghan was definitely slipperier, so that I needed a surgeon's knot.)
It's funny how things can come full circle and all for the better. I have also been hand tensioning these afghan warps, because I don't have enough half gallon milk jugs to use as weights. So even with techniques I thought I had abandoned, my warp tension has been good. It is rewarding to know that I can get the same results either way. It's a real confidence booster. Plus, now I'll always have a good answer for my DH when he asks, "Who's winning, you or the warp?"
P.S. to this post's comments. Susan's blog can be found at Centerweave.